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Theorem funcnv0 6634
Description: The converse of the empty set is a function. (Contributed by AV, 7-Jan-2021.)
Assertion
Ref Expression
funcnv0 Fun

Proof of Theorem funcnv0
StepHypRef Expression
1 fun0 6633 . 2 Fun ∅
2 cnv0 6163 . . 3 ∅ = ∅
32funeqi 6589 . 2 (Fun ∅ ↔ Fun ∅)
41, 3mpbir 231 1 Fun
Colors of variables: wff setvar class
Syntax hints:  c0 4339  ccnv 5688  Fun wfun 6557
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-mo 2538  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-id 5583  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-fun 6565
This theorem is referenced by:  f10  6882  pthdlem1  29799  0trl  30151  0pth  30154
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